In: Statistics and Probability
Given a random sample of size 16 from a normally distributed population with a mean of 100 and standard deviation of 24, find P(x bar≤90)
Solution :
Given that,
mean = 
 = 100
standard deviation = 
 = 24
n = 16

= 100

= 
 / 
n = 24 
16 = 6
p ( 
  90
)
P ( 
 - 
/
)  
( 90 - 100 / 6)
P( z  
- 10 / 6 )
P ( z 
 -1.67 )   
Using z table
= 0.0475
Probability = 0.0475